Extend the weighted multi-defect construction to higher genus

Extend the weighted multi-defect construction for conical defects in Jackiw–Teitelboim BF gravity from genus zero to higher genus, including the associated weighted moduli-space geometry and amplitudes.

Background

The paper develops the weighted multi-defect construction explicitly only for genus-zero amplitudes. Although the BF defect correlators can be defined at arbitrary genus, extending the weighted compactification and its amplitude calculations to higher-genus surfaces is left unresolved. This problem is important for obtaining a full topological expansion of the defect-deformed JT theory beyond the genus-zero cluster expansion.

References

Although the BF defect correlators can be defined at arbitrary genus, we carry out the weighted multi-defect construction explicitly only at genus zero. A systematic extension to higher genus remains open.

— Conical Defects in JT Gravity from BF Theory: Quantization, Fusion, and Weighted Moduli Spaces  (2609.03347 - Gu, 3 Sep 2026) in Section 1, Introduction (following the discussion of the gravitational integration cycle)